A cubic dissipative coefficient results for example when the inflaton couples to the light degrees of freedom (dof) through a heavy mediator. This pattern directly protects the inflaton potential from acquiring large thermal corrections that might spoil inflation, but typically requires a too large no. of light and mediator fields in order to get enough dissipation. Instead the inflaton potential can be shielded against large radiative corrections by the use of symmetries. When coupled directly to fermionic light dof this leads to a linear dissipative coefficient in the so-called “Warm Little Inflation” (WLI) model [1]}, [2]}, [3]}; an axion-like coupling to Yang-Mills fields gives again \(\Upsilon \sim T^3\)  in the “Minimal Warm Inflation” (MWI) model [4]}; while replacing fermionic by light scalar dof in the WLI give rise to and inverse dissipative coefficient \(\Upsilon \sim 1/T\)  [5]}. In the latter case, we have “light” particles when their masses \(m_i\)  are below \(T\) , but as inflation proceeds and \(T\)  decreases, by the end of inflation we may have \(m_i \gg T\) , and \(\Upsilon \sim T^\kappa \)  with \(\kappa >0\) . While an inverse dissipative coefficient is free of the problems of the growing mode at CMB scales, before the end of inflation we recover the enhancement of the spectrum and the prospects to have PBHs and non-negligible GWs. This is the pattern that we want to study in this paper.
